State Sen. Chris McDaniel said Wednesday that his campaign team plans to investigate “irregularities” in the primary race, as it considers whether to pursue some sort of legal challenge after his razor-thin loss to incumbent U.S. Sen. Thad Cochran in a Republican runoff a day earlier.

Mr. McDaniel and his tea party allies also continued to blast establishment Republicans for relying on Democrats to put Mr. Cochran over the line in the open contest.

“If our party and our conservative movement are to coexist, it is paramount that we ensure the sanctity of the election process is upheld,” Mr. McDaniel said. “And we will do that. In the case of yesterday’s election, we must be absolutely certain that our Republican primary was won by Republican voters.

“In the coming days, our team will look into the irregularities to determine whether a challenge is warranted,” Mr. McDaniel said. “After we’ve examined the data, we will make a decision about whether and how to proceed.”

Others said the race was over.

Former Mississippi Gov. Haley Barbour, who fought tenaciously to keep Mr. Cochran in office, said voters made a politically savvy choice in renominating Mr. Cochran, who eked out a victory with the help of black voters, whom he aggressively courted in the final weeks of the campaign.

“I think Cochran’s chances of re-election are far greater than his opponent’s — far greater,” Mr. Barbour, a former head of the Republican National Committee, said on CNBC’s “Squawk Box.”

In the wake of the result, Judson Phillips, the head of Tea Party Nation, called on Mr. McDaniel to wage a write-in campaign. He said the race showed that the [Republican in name only] wing of the party will do whatever is in its power — even reach out to Democrats — to stay in power.

“When the Republican Establishment acts like Democrats, what is the point of supporting them?” Mr. Phillips said in an early morning email blast. “The answer is, we don’t have to.”

But a Republican operative said that under Mississippi law the only way that could happen is if Mr. Cochran died between the time the general election ballots were printed and Election Day.

“I think right now they are looking at all their options, which are somewhat limited given our election laws in this state,” the operative said, alluding to the McDaniel camp.